At high energy the standard model possesses conformal symmetry at the classical level. This is reflected at the quantum level by relations between the different beta functions of the model. These relations are known as the Weyl consistency conditions. We show that it is possible to satisfy them order by order in perturbation theory, provided that a suitable coupling constant counting scheme is used. As a direct phenomenological application, we study the stability of the standard model vacuum at high energies and compare with previous computations violating the Weyl consistency conditions.
Antipin, O., Gillioz, M., Krog, J., Mølgaard, E., & Sannino, F. (2013). Standard Model Vacuum Stability and Weyl Consistency Conditions. Journal of High Energy Physics (JHEP), 2013(34). https://doi.org/10.1007/JHEP08(2013)034